Sound speed in pure water. Marczak equation
Mathematical definition
$$\boxed{C\left( T \right) = {k_0} + {k_1}T + {k_2}{T^2} + {k_3}{T^3} + {k_4}{T^4} + {k_5}{T^5}}$$
Notation |
Description |
Units |
Limits |
$C$ |
sound speed |
$\text{m/s}$ |
|
$T$ |
temperature |
$^{\circ}\text{C}$ |
$0 < T < 95$ |
Coefficient |
Value |
$k_{0}$ |
$+1.402385 \times 10^{3}$ |
$k_{1}$ |
$+5.038813$ |
$k_{2}$ |
$-5.799136 \times 10^{-2}$ |
$k_{3}$ |
$+3.287156 \times 10^{-4}$ |
$k_{4}$ |
$-1.398845 \times 10^{-6}$ |
$k_{5}$ |
$+2.787860 \times 10^{-9}$ |
Octave/Matlab implementation
function C = sound_speed_water_marczak(T)
% Inputs
% T: temperature \ degree Celsius \ 0 < T < 95
% Outputs
% C: speed of sound in pure water \ m/s
k0 = +1.402385e+3;
k1 = +5.038813e+0;
k2 = -5.799136e-2;
k3 = +3.287156e-4;
k4 = -1.398845e-6;
k5 = +2.787860e-9;
C = k0*(T.^0) + k1*(T.^1) + k2*(T.^2) ...
+ k3*(T.^3) + k4*(T.^4) + k5*(T.^5);
end
Computational examples
![](../img/sound_speed_water_marczak.en-1.png)
References
- Marczak, Wojciech, "Water as a standard in the measurements of speed of sound in liquids", 1997